A closed box with a square base is to have a volume of 16,000 cubic centimeters.

Question

A closed box with a square base is to have a volume of 16,000 cubic centimeters. The material for the top and bottom of the box costs $3 per square centimeter and the material for the sides costs $1.50 per square cm. Let x be the length of one edge of the base of the box, in cm. a) Let C denote the cost, in dollars, of material for the box. Write a formula for C in terms of only x. b) Determine the dimensions of the cheapest box. You need to use the appropriate derivative function to locate critical points for the cost function

Explanation / Answer

If the base square's side has a length of a centimeters, then the volume is

a*a*h = 16000

Therefore, h = 16000/a

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